In a medium bowl, combine the apple butter, barbecue sauce, apple cider vinegar, garlic powder, onion powder, black pepper, and salt. Stir until smooth and well blended.
Place the chicken breasts in the slow cooker. Pour the prepared sauce over the chicken, making sure each piece is coated evenly. Cover and cook on low for 6-7 hours or on high for 3-4 hours until the chicken is tender and shreds easily.
Once cooked, remove the chicken breasts and shred them using two forks. Return the shredded chicken to the slow cooker, mixing it well with the remaining sauce to soak up all the flavors.
In a separate bowl, combine the coleslaw mix, mayonnaise, apple cider vinegar, and sugar. Toss until the slaw is evenly coated. Adjust seasoning to taste, adding more sugar or vinegar if needed.
Split the whole grain rolls and toast lightly if desired. Pile the pulled chicken generously onto the bottom half of each roll, then top with a heap of the fresh coleslaw. Place the top half of the roll on and press gently.
Serve immediately with your favorite sides.